Question

This figure shows the interaction of a cation with surrounding water molecules. Would you expect the energy of ion-solvent interaction to be greater for \(\mathrm{Na}^{+}\) or \(\mathrm{Li}^{+}\) ? Explain. [Section 13.1]

Short answer

The energy of ion-solvent interaction would be greater for \(\mathrm{Li}^{+}\) compared to \(\mathrm{Na}^{+}\) due to its smaller size and shorter distance to the surrounding water molecules, resulting in a stronger ion-dipole interaction.

Step-by-step solution

Briefly describe ion-solvent interactions

When a cation interacts with surrounding water molecules, it attracts the negatively charged oxygen atoms in water molecules, forming an ion-dipole interaction. This interaction is the basis of solvation, or the process by which the solute is surrounded by solvent molecules. The strength of this interaction is determined by the charge of the ion and the distance between the ion and the negatively charged atoms in the solvent.

Compare the relative sizes of \(\mathrm{Na}^{+}\) and \(\mathrm{Li}^{+}\) cations

In order to determine the strength of ion-solvent interactions for these two cations, we need to consider their relative sizes. \(\mathrm{Li}^{+}\) has a smaller atomic radius compared to \(\mathrm{Na}^{+}\). This means that \(\mathrm{Li}^{+}\) is a smaller ion and can come closer to the surrounding water molecules.

Discuss the influence of ion size on ion-solvent interaction energy

Since \(\mathrm{Li}^{+}\) is smaller than \(\mathrm{Na}^{+}\), the distance between \(\mathrm{Li}^{+}\) and the oxygen atom of the surrounding water molecules is shorter. This shorter distance results in a stronger ion-dipole interaction between \(\mathrm{Li}^{+}\) and water, leading to a higher energy of ion-solvent interaction.

Conclusion

Based on the analysis of ion size and its influence on ion-solvent interaction energy, we can conclude that the energy of ion-solvent interaction would be greater for \(\mathrm{Li}^{+}\) compared to \(\mathrm{Na}^{+}\) because of its smaller size and shorter distance to the surrounding water molecules, which results in a stronger ion-dipole interaction.

Key concepts

Solvation Process

When we dissolve substances like salts in a solvent such as water, we witness the solvation process. This process plays a vital role in chemistry and various biological systems. Solvation involves the attraction and association of solvent molecules to ions or other solutes. In water, solvation is often called hydration.

For example, when table salt (sodium chloride, NaCl) is added to water, the positively charged sodium ions (Na^{+}) and negatively charged chloride ions (Cl^{-}) are separated and surrounded by water molecules. The slightly positive hydrogen atoms in water molecules are attracted to the chloride ions, while the slightly negative oxygen atoms orient themselves around the sodium ions. This interaction allows the ions to be dispersed throughout the solution, making it homogeneous.

The efficiency and extent of solvation depend on factors like temperature, solute and solvent types, and especially the solvent's polarity. Water is an excellent solvent due to its high polarity and ability to solvate ions effectively.

Ion-Dipole Interaction

Ionic compounds dissolve in water mainly through ion-dipole interactions. An ion-dipole interaction is an attractive force that occurs between an ion and a polar molecule. In this case, the polar water molecules have a partial negative charge on the oxygen atom and a partial positive charge on the hydrogen atoms. These result from differences in electronegativity between the hydrogen and oxygen atoms.

When an ionic compound like NaCl is added to water, the sodium ions (Na^{+}) are attracted to the negatively charged oxygen, and the chloride ions (Cl^{-}) are attracted to the positively charged hydrogen atoms in water molecules. This interaction stabilizes the ions in solution and is stronger when either the charge of the ions is higher or the ions are closer to the water molecules, allowing for stronger attractions.

Atomic Radius

The atomic radius refers to the size of an atom and plays a critical role in understanding chemical reactions and properties. It is usually measured from the center of the nucleus to the boundary of the surrounding cloud of electrons. As we move across the periodic table from left to right, the atomic radius generally decreases because the number of protons increases, pulling the electron cloud closer to the nucleus.

In the context of ion-solvent interactions, smaller ions, like lithium (Li^{+}), have a smaller atomic radius compared to larger ions like sodium (Na^{+}). This smaller size allows them to engage more closely and intimately with solvent molecules. The smaller atomic radius leads to a greater charge density, which intensifies the ion-dipole interactions when an ion dissolves in a polar solvent such as water.

Chemical Interactions

Chemical interactions encompass various forces that hold atoms and molecules together, including ionic, covalent, and metallic bonds, as well as intermolecular forces like hydrogen bonding, dipole-dipole interactions, and London dispersion forces.

In a solvation process, the key chemical interactions are those between the ions and the solvent molecules. For cations like Li^{+} and Na^{+}, the ion-dipole interactions are paramount. These interactions are a type of electrostatic attraction, which is the force that holds oppositely charged particles together in ionic compounds. In solution, they can result in a stable configuration where every ion is surrounded by solvent molecules, decreasing the potential energy of the system.

Understanding these interactions is not only crucial for chemistry but also for fields like materials science, pharmacology, and environmental science, where solvation effects are important in the behavior of substances.